Families of cuts with the MFMC-property

Abstract

A family ℱ of cuts of an undirected graphG=(V, E) is known to have the weak MFMC-property if (i) ℱ is the set ofT-cuts for someTV with |T| even, or (ii) ℱ is the set of two-commodity cuts ofG, i.e. cuts separating any two distinguished pairs of vertices ofG, or (iii) ℱ is the set of cuts induced (in a sense) by a ring of subsets of a setTV. In the present work we consider a large class of families of cuts of complete graphs and prove that a family from this class has the MFMC-property if and only if it is one of (i), (ii), (iii).

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Karzanov, A.V. Families of cuts with the MFMC-property. Combinatorica 5, 325–335 (1985). https://doi.org/10.1007/BF02579247

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AMS subject classification (1980)

  • 68 E 10
  • 05 C 99